There are no arguments.
Returns the index of the current row in the partition. Example (for the first row in the partition): INDEX( ) = 1
IF INDEX() = 1 THEN "I am the first row in the partition" ELSE "I am not" END
INDEX can be looked at as the "rank" function. (See other rank articles.) "Compute Using" defines the partition within which INDEX will count from 1 to N.
It is also useful on the path shelf when your level of detail causes the marks to be dots instead of line when the mark type is set to Line, and you do not have another field to connect the dots in order.
see comment at http://www.tableausoftware.com/forum/version-6-table-calcs-understanding-few-basics#comment-37271 for an example.